Numerical study of turbulent two-phase Couette flow

Size: px
Start display at page:

Download "Numerical study of turbulent two-phase Couette flow"

Transcription

1 Center for Turbulence Research Annual Research Briefs Numerical study of turbulent two-phase Couette flow By A.Y. Ovsyannikov, D. Kim, A. Mani AND P. Moin 1. Motivation and objectives The motivation underpinning this work is the need to understand bubble generation mechanisms due to interactions between free surface and turbulent boundary layers as commonly seen near ship walls. As a canonical problem, we consider a turbulent plane Couette flow with vertical parallel sidewalls and an air-water interface established by gravity in the vertical direction. Two-phase Couette flow has been described in the literature in different flow setups. Most studies were limited to cases of low Reynolds number and the evolution of a single bubble/droplet. Deformation and breakup of a single droplet in a plane Couette flow at low Reynolds number has been studied experimentally, theoretically, and numerically (see e.g., Li et al. 2000; Renardy et al. 2002; Rallison 1984). In another example of the two-phase Couette flow is the two-layers of immiscible fluids which are set between moving horizontal walls. Due to viscosity difference between fluids, there is a jump in the tangential velocity gradient across the interface which induces instabilities at the fluid interface (Coward et al. 1997; Charru & Hinch 2000). At high Reynolds number, there are only a few studies of two-phase Couette flow. Iwasaki et al. (2001) studied the dynamics of a single immiscible drop in turbulent gas flow between two moving walls. Fulgosi et al. (2003); Liu et al. (2009) performed direct numerical simulation (DNS) of interface evolution in Couette flow between two moving horizontal walls. One interesting case of a two-phase Couette flow in a turbulent regime is when the initial interface is set to be orthogonal to the moving vertical walls. In such a setup, the interaction between the fluid interface and the turbulent boundary layer is a key phenomenon. At sufficiently high Reynolds, Weber and Froude numbers, shearinduced interfacial waves can break, which leads to the formation of air cavities. These air cavities will be further fragmented by turbulence to smaller bubbles. These complexities make two-phase Couette flow at high Reynolds number a challenging problem for both experiments and numerical analysis. Capturing the small-scale flow and interface features requires high-resolution experimental techniques and very expensive DNS calculations. Only two numerical studies (Kim et al. 2012, 2013) have been performed for investigation of air entrainment and bubble generation in two-phase Couette flow. The current work is a continuation of our recent studies (Kim et al. 2012, 2013), where we performed numerical simulations of the interface breakup in two-phase Couette flow at Reynolds number of approximately and Weber number of approximately (surface tension coefficient was much smaller than the realistic value for an air-water system). The effect of Froude number on the interface breakup and bubble generation was studied in Kim et al. (2012). The second paper of Kim et al. (2013) was mostly devoted to the development and assessment of a mass conservative interface-capturing method based on a geometric volume-of-fluid (VOF) approach, and one simulation of Cascade Technologies Inc.

2 42 Ovsyannikov et al. g Figure 1. Schematic illustration of the flow geometry. the two-phase Couette flow was performed for a Reynolds number of and a Weber number of 200. However, there have been no studies with one-to-one matched experiments and numerical simulations. The primary objective of this work is to perform a numerical simulation of a two-phase Couette flow with flow parameters very close to those of the laboratory experiment conducted by our collaborators (the group of Dr. James Duncan at the University of Maryland). The bubble formation rate, bubble size distribution, and the effect of interface on the modulation of turbulence are the main characteristics of this flow type, and our investigations are focused on understanding these characteristics. This paper is structured as follows. In Section 2 we present the equations for the problem and discuss the key dimensions chosen for our simulations, grid resolution requirements and details of the numerical method. Preliminary results of the numerical simulation are presented and analyzed in Section 3. In Section 4 we show the effect of water depth on air entrainment. Finally, conclusions are summarized in Section Problem formulation We perform a simulation of a two-phase system with realistic air/water density and viscosity ratios. The density of liquid is ρ liq = 1000kg/m 3 and the density of gas is ρ gas = 1.2kg/m 3. However, to reduce computational cost, the viscosity of gas and liquid are increased four times compared to their realistic values. Thus the viscosity of the gaseous phase is µ gas = Pa s and the viscosity of the liquid phase is µ liq = Pa s. The surface tension coefficient σ and gravity acceleration g take realistic values of 0.07N/m and 9.81m/s 2, respectively. Figure 1 depicts the schematic of the flow configuration and domain size. The computational domain is a rectangular box with sizes 2πh, 2h and 6h in the streamwise (x), wall-normal (y) and spanwise (z) directions, respectively. Here h = 2 cm is the half-distance between walls. Initially, the interface is located at a plane z = 4h, hence a height of liquid layer H liq is 4h and a height of gas layer H gas is 2h. The sidewalls are moving in the opposite directions with speed of U w = 1.6m/s. Based on the chosen parameters, the following main dimensionless

3 Numerical study of turbulent two-phase Couette flow 43 Re We Fr ρ liq /ρ gas µ liq /µ gas H liq /h Simulation (Kim et al. 2012) , Simulation (Kim et al. 2013) Exp. (Masnadi et al. 2013) Exp. (Washuta et al. 2014) Present simulation Table 1. Flow configurations for two-phase turbulent Couette flow from experimental and numerical studies. In Masnadi et al. (2013), dimensionless parameters were defined in a different way. Here we recompute all parameters according to Eq. (2.1). parameters are Re = ρ liqu w h, We = ρ liquw 2h, Fr = U w, ar = H liq µ liq σ gh h, (2.1) which are Reynolds, Weber, Froude numbers, and aspect ratio (ratio of water depth to h), respectively. All non-dimensional groups are determined using properties of the liquid phase. In the current study, Re = 8000, We = 730, Fr = 3.6 and ar = 4. Table 1 summarizes recent experiments and numerical studies on the two-phase Couette flow problem in turbulent regime. The experiments reported in Table 1 are all performed by Masnadi et al. (2013) in a 7.5m 0.075m 1m air-water channel at different operating parameters. In their setup one wall is stationary and the other is moving. The belt velocity is varied in a range from 2.5 to 4.0m/s, leading to a range of Reynolds numbers from to 74750, Weber numbers from 837 to 2142, and Froude numbers from 2.06 to Note that there have been no studies with one-to-one matched experiments and numerical simulations, in particular concerning the matching of such key dimensionless parameters as Re, We and Fr. In the present work we selected these parameters in accordance with the experiments being performed currently by our collaborators for a channel of width h = 2cm (Washuta et al. 2014) and Reynolds number of 32000, Weber number of 730 and Froude number of 3.6. These match with the experiment in the narrow channel Weber and Froude numbers, density and viscosity ratios; however, the Reynolds number is four times lower in our numerical study. We expect that a four fold difference in Reynolds number should not be critical in predicting bubble generation due to the large difference between turbulent and interfacial length scales (see paragraph 2.3 for an estimation of Kolmogorov and Hinze scales). Also, the aspect ratio in simulations is much smaller than in experiments Governing equations and numerical method The governing equations describing the motion of two immiscible, incompressible Newtonian fluids are the conservation of mass and momentum. The first equation is given in terms of the volume fraction function ψ as ψ t + (ψu) = 0, (2.2)

4 44 Ovsyannikov et al. and the second is ρu t + (ρuu) = p+ τ +ρg+f st, (2.3) where u is the velocity, p is the pressure, ρ is the density, τ = µ( u + u T ) is the shear stress tensor, µ is the dynamic viscosity, g is the acceleration due to gravity and F st = σκδ Σ n is the surface tension force. Here, σ is the surface tension coefficient, δ Σ is the Dirac delta function, κ is the interface curvature, and n is the interface normal vector. The volume fraction function ψ is equal to 1 in the gas phase and 0 in the liquid phase. The interface is then represented by the volume fraction values, 0 < ψ < 1. In the case of a two-phase flow with immiscible fluids, the density and dynamic viscosity are the stepwise functions and can be written in terms of ψ, ρ(x,t) = ρ gas ψ(x,t)+ρ liq [1 ψ(x,t)], (2.4) µ(x,t) = µ gas ψ(x,t)+µ liq [1 ψ(x,t)]. (2.5) For discretization of Eqs. (2.2)-(2.3), we use numerical schemes as described in Kim et al. (2013). In brief, we use the finite-volume pressure-correction method, where the interface dynamics is captured by the volume-of-fluid method. Geometric flux reconstruction is based on a piecewise line interface calculation (PLIC) algorithm. The VOF method conserves the mass of each phase within machine precision, and this is essential for simulation of two-phase flows at high Reynolds and Weber numbers. The surface tension force is computed using the continuum surface force model (Brackbill et al. 1992) coupled with the balanced force method (Francois et al. 2006). For an accurate calculation of interface normal vector and curvature, a level set function is used which is reconstructed from the ψ field at every timestep using a fast marching method (Sethian 1999) Initial and boundary conditions The flow is assumed to be statistically homogeneous in the streamwise x direction where periodic boundary conditions are used. On the side counter-moving walls (y = ±h), we use no-slip boundary conditions. On the top and bottom walls (z = 0 and z = 6h), we use slip boundary conditions. On all solid wall boundaries, no-flux conditions are used for the volume fraction function. As the initial condition, we use a laminar velocity profile perturbed by 10% noise. The initial value for ψ corresponds to the flat shape of the interface Grid resolution requirement In order to accurately capture the interface dynamics, we need to resolve the typical interface scale (r cr ) and turbulent scales (η and δ ν ) Turbulent lengthscale The Kolmogorov lengthscale is given by η = (ν 3 /ε) 1/4 110µm. (2.6) Hereεisthemeanenergydissipationrateperunitmassanditcanbeestimatedaccording to ui ε = ν + u 2 j U w u 2 τ 0.5m 2 s 3, (2.7) x j x i h

5 Numerical study of turbulent two-phase Couette flow 45 where u τ = (τ w /ρ) 1/2 is the friction velocity, and τ w = µ U y is the wall shear stress. The viscous lengthscale is defined as follows δ ν = ν/u τ 60µm. (2.8) Here, for simplicity, we dropped the subscripts, and all quantities ρ, µ, ν and ε are based on properties of the liquid phase Interface lengthscale In addition to turbulent lengthscales, we need to resolve an interfacial lengthscale (bubble radius) in two-phase simulations. There are two major mechanisms of bubble formation: turbulent fragmentation(kolmogorov 1949; Hinze 1955) and instability of the air film due to liquid-liquid impact (Esmailizadeh & Mesler 1986; Pumphrey & Elmore 1990). In our simulations we resolve only the bubbles due to the first mechanism. This lengthscale can be estimated using the Kolmogorov-Hinze theory. We apply this theory to estimate the breakage of bubbles in a turbulent liquid flow. If the bubble diameter is larger than the Kolmogorov lengthscale, then the critical bubble radius (referred to as the Hinze scale) is given by r cr = 2 8/5 ( σwecr ρ liq ) 3/5 ε 2/5 if 2r cr > η. (2.9) If the bubble diameter is smaller than the Kolmogorov lengthscale, then the critical bubble radius is given by ( ) 1/3 σwecr r cr ε 1/3 if 2r cr < η. (2.10) ρ liq In our case, the Hinze scale is much larger than the Kolmogorov lengthscale and the critical bubble radius is given by Eq. (2.9). For critical Weber number 4.7 (according to Deane & Stokes 2002), the critical bubble radius is r cr 3mm η. Therefore, we choose conventional DNS resolution as in single-phase flows. We use a Cartesian grid with uniform mesh spacing in x and z directions, and stretched mesh in the y direction according to N y 1 )) y j = htanh( γ( 1+ 2(j 1) tanh(γ), (2.11) where the stretching parameter γ is 2.9. Based on the viscous lengthscale in the liquid phase the grid resolution is x + 13, y + min 0.2, y+ max 13 and z + 7. Such discretization results in at least 4 grid points per Hinze scale (8 points per bubble diameter) and 18 grid points per viscous sublayer. Finally, the timestep is given from the stability constraint due to surface tension as it is more restrictive than the stability conditions due to convection and gravity terms (the viscous terms are treated implicitly): 3. Results t = ρliq +ρ gas 4πσ y 3/2 min 10 6 s. (2.12) To get a statistically developed flow we run the simulations for about 100 flow-through times. Figure 2 and Figure 2 show the time histories of the potential energy due

6 46 Ovsyannikov et al. Figure 2. Time history of potential energy due to gravity, E g = ρ(x,t)g xdx; V normalized area of the air-water interface A/A 0, where A = δ(φ) φ dx, φ is the level-set V function. The gray box depicts a statistical sampling window. to gravity and the total area of the air-water interface, respectively. Figure 2 shows that it takes about 70 flow-through times to achieve fully developed state, after which turbulent statistics are collected over 30 flow-through times (this region is depicted by the gray box). The maximum potential energy is about 1.3% of the initial value at the time of maximum deformation (around 15 flow-through times), and it is about 0.4% higher than its initial value at the fully developed state. Figure 2 shows the evolution of the gas-liquid interface area. Due to interface corrugation and generation of bubbles, the total area of the interface increases about 22 times compared to the initial area of the unperturbed interface. Figure 3(a-d) show instantaneous snapshots of the interface (given by iso-surface ψ = 0.5). On the free surface, shear-induced oblique wave structures are observed (Figure 3), then the interfacial waves grow in amplitude (Figure 3), leading to breakup of the interface (Figure 3(c)). The air cavities are found underneath the free surface, trapped between the breaking interfacial waves. These air cavities are subsequently fragmented into air bubbles in the water. Finally, Figure 3(d) shows the interface at the fully developed state. Figure 4 shows time- and streamwise-averaged flow for two cases: a two-phase Couette flow and a single-phase Couette water flow at the same Reynolds number of The color contours correspond to the streamwise component of the mean velocity, ū, while the wall-normal and spanwise components, ( v, w), are shown as vector plot. The maximum root-mean-square (rms) value of in-plane velocities represents (after 100 flow-through times) approximately 6-7% of the maximum streamwise velocity for both cases and does not diminish with time. For the single-phase Couette flow, secondary flow is represented by four large eddies, while for the two-phase case the secondary flow is more complex due to the effects of the interface. In our simulations the length of the computational domain, 2πh, was chosen as in classical simulations of pressure-driven channel flow. However, it is known from studies of single-phase Couette flow (Lee & Kim 1991; Komminaho et al. 1996; Papavassiliou & Hanratty 1997) that the domain length should be much longer. In this work we focus on a study of interface/boundary layer interaction and leave the study of Couette flow in longer channels for future research. Mean streamwise velocity profiles measured at z/h = 1.5, z/h = 2.5, z/h = 3.5 and z/h = 4 locations are shown in Figure 5. In addition to two-phase Couette results,

7 Numerical study of turbulent two-phase Couette flow 47 (c) (d) Figure 3. Snapshots of the air-water interface at different times: t = 5; t = 10; (c) t = 15; (d) t = 60. we show the result of simulation for single-phase Couette flow at the same Reynolds number of Figure 5 shows velocity profiles in non-dimensional units, U/U w versus y/h. Figure 5 shows the same data in non-dimensional viscous units according to U + = (U U w )/u τ and y + = (h y)/δ ν. As seen from Figure 5, there is no collapse of the results for two-phase Couette flow with the log-law even for a velocity profile quite far from the interface at z/h = 1.5. Even for single-phase Couette flow, a particular profile of streamwise velocity does not necessarily collapse with the log-law owing to the presence of persistent roller structures. Only after averaging of velocity in a vertical direction does the velocity profile for single-phase Couette flow matches with the log-law. Figure 6 shows the rms value of the streamwise turbulent intensity. The 2D field of the turbulent fluctuations is presented on the left, while 1D profiles at different locations z/h = 1.5, z/h = 2.5, z/h = 3.5 and z/h = 4 are presented on the right. Compared

8 48 Ovsyannikov et al. Figure 4. Turbulent statistics: time- and streamwise-averaged velocity field. Color plot shows the mean streamwise velocity; vector plot depicts mean in-plane flow. Two-phase Couette flow at Re = 8000, We = 730 and Fr = 3.6; Single-phase Couette flow at Re = Figure 5. Turbulent statistics for two-phase Couette flow at Re = 8000, Fr = 3.6, We = 730: mean streamwise velocity; mean streamwise velocity in viscous units. Lines represent profiles at different depths:, z/h = 4;, z/h = 3.5;, z/h = 2.5;, z/h = 1.5. Symbols correspond to DNS results (also averaged in the vertical direction) for single-phase Couette water flow at the same Reynolds number. to single-phase Couette flow at z/h = 4, amplification of turbulent intensity was found near the interface, whereas a diminished turbulent intensity was observed in the core region. Figure 7 and Figure 8 show rms values of the wall-normal and spanwise turbulent intensities, respectively. Note that for wall-normal and spanwise turbulent intensities, turbulence near the wall and near the interface (profile at z/h = 4) increases compared

9 Numerical study of turbulent two-phase Couette flow 49 Figure 6. Turbulent statistics: rms of the streamwise velocity fluctuation. 2D field; 1D profiles at different depths:, z/h = 4;, z/h = 3.5;, z/h = 2.5;, z/h = 1.5. Symbols correspond to DNS results for single-phase Couette water flow. Figure 7. Turbulent statistics: rms of the wall-normal velocity fluctuation. 2D field; 1D profiles at different depths:, z/h = 4;, z/h = 3.5;, z/h = 2.5;, z/h = 1.5. Symbols correspond to DNS results for single-phase Couette water flow. to turbulent intensity at other depths. However, the absolute value of turbulent intensity is larger for single-phase Couette flow.

10 50 Ovsyannikov et al. Figure 8. Turbulent statistics: rms of the vertical velocity fluctuation. 2D field; 1D profiles at different depths:, z/h = 4;, z/h = 3.5;, z/h = 2.5;, z/h = 1.5. Symbols correspond to DNS results for single-phase Couette water flow. Figure 9. Air-water interface at fully developed state: Results for an aspect ratio of 1.57 and Re = 12000, We = 206, Fr = 3.8 (Kim et al. 2013); Present results for an aspect ratio of 4 and Re = 8000, We = 730, Fr = Influence of the water depth Figure 9 shows a comparison of the fully developed air-water interface from our previous results (Kim et al. 2013) (Figure 9) and the current simulation (Figure 9). The results on the left figure were obtained for an aspect ratio of 1.57, whereas in the current simulation the aspect ratio is 4. As seen, the simulation for the higher value of the aspect ratio predicts much less air entrainment. To confirm our hypothesis of the influence of the water depth on bubble density, we are currently running simulations for low and high values of the aspect ratio (1.57 and 8) for the same non-dimensional parameters: Reynolds, Weber and Froude numbers, as in the simulation presented in this work.

11 5. Conclusions Numerical study of turbulent two-phase Couette flow 51 In this work we performed a numerical simulation of a two-phase Couette flow at a Reynolds number of 8000, Froude number of 3.6, Weber number of 730 and at realistic air-to-water density and viscosity ratios. Except for Reynolds number and water depth, the parameters of simulation correspond to experiments currently being performed at the University of Maryland. The VOF method has been used to predict interface dynamics. To achieve statistically state, two-phase simulations of Couette flow require much longer time compared to simulations of single-phase Couette flow. Amplification of turbulent intensity was found near the interface, whereas diminished turbulent intensity was observed in the core region. It was found that the bubble density depends on the water depth. To validate this result, in our ongoing work we compare numerical results obtained for different aspect ratios with experimental data. In addition, a simulation is being carried out with deeper water at an aspect ratio H liq /h of 8 and the same non-dimensional parameters, Re = 8000, We = 730, Fr = 3.6. Acknowledgments The authors would like to express their gratitude to Dr. Ivan Bermejo-Moreno for his useful comments. The financial support of the Office of Naval Research is gratefully acknowledged. The authors also acknowledge computing time on the Mira cluster at Argonne Leadership Computing Facility(ALCF) and on the Certainty cluster at Stanford (MRI-R2 NSF Award ). REFERENCES Brackbill, J., Kothe, D. & Zemach, C A continuum method for modeling surface tension. J. Comput. Phys. 100, Charru, F. & Hinch, J. E Phase diagrama of interfacial instabilities in a twolayer Couette flow and mechanism of the long-wave instability. J. Fluid Mech. 414, Coward, A. V., Renardy, Y. Y., Renardy, M. & Richards, J. R Temporal evolution of periodic disturbances in two-layer Couette flow. J. Comput. Phys. 132, Deane, G. B. & Stokes, M. D Scale dependence of bubble creation mechanisms in breaking waves. Nature 418, Esmailizadeh, L. & Mesler, R Bubble entrainment with drops. J. Colloid Interface Sci. 110, Francois, M. M., Cummins, S. J., Dendy, E. D., Kothe, D. B., Sicilian, J. M. & Williams, M. W A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213, Fulgosi, M., Lakehal, D., Banerjee, S. & De Angelis, V Direct numerical simulation of turbulence in a sheared air-water flow with a deformable interface. J. Fluid Mech. 482, Hinze, J Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, Iwasaki, T., Nishimura, K., Tanaka, M. & Hagiwara, Y Direct

12 52 Ovsyannikov et al. numerical simulation of turbulent Couette flow with immiscible droplets. Int. J. Heat Fluid Flow 22, Kim, D., Mani, A. & Moin, P.2012Numericalsimulationofwavebreakinginturbulent two-phase Couette flow. Annual Research Briefs, Center for Turbulence Research, Stanford University, pp Kim, D., Mani, A. & Moin, P Numerical simulation of bubble formation by breaking waves in turbulent two-phase Couette flow. Annual Research Briefs, Center for Turbulence Research, Stanford University, pp Kolmogorov, A On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk. SSSR 66, Komminaho, J., Lundbladh, A. & Johansson, A. V Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, Lee, M. & Kim, J The structure of turbulence in a simulated plane Couette flow. In Eighth Symp. on Turbulent Shear Flows, pp Li, J., Renardy, Y. Y. & Renardy, M Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Phys. Fluids 12, Liu, S., Kermani, A., Shen, L. & Yue, D. K. P Investigation of coupled airwater turbulent boundary layers using direct numerical simulations. Phys. Fluids 21, Masnadi, N., Washuta, N., Wang, A. & Duncan, J The interaction of a turbulent ship-hull boundary layer and a free surface. Bull. Am. Phys. Soc. 58. Papavassiliou, D. V. & Hanratty, T. J Interpretation of large-scale structures observed in a turbulent plane Couette flow. Int. J. Heat Fluid Flow 18, Pumphrey, H. C. & Elmore, P. A.1990The entrainmentofbubbles bydropimpacts. J. Fluid Mech. 220, Rallison, J The deformation of small viscous drops and bubbles in shear flows. Ann. Rev. Fluid Mech. 16, Renardy, Y., Cristini, V. & Li, J Drop fragment distributions under shear with inertia. Int. J. Multiphase Flow 28, Sethian, J Fast marching methods. SIAM Review 41, Washuta, N., Masnadi, N. & Duncan, J The turbulent boundary layer on a horizontally moving, partially submerged, surface-piercing vertical wall. In Symposium on Naval Hydrodynamics,, pp

Numerical simulation of wave breaking in turbulent two-phase Couette flow

Numerical simulation of wave breaking in turbulent two-phase Couette flow Center for Turbulence Research Annual Research Briefs 2012 171 Numerical simulation of wave breaking in turbulent two-phase Couette flow By D. Kim, A. Mani AND P. Moin 1. Motivation and objectives When

More information

The JHU Turbulence Databases (JHTDB)

The JHU Turbulence Databases (JHTDB) The JHU Turbulence Databases (JHTDB) TURBULENT CHANNEL FLOW AT Re τ = 5200 DATA SET Data provenance: M. Lee 1 & R. D. Moser 1 Database ingest and Web Services: Z. Wu 2, G. Lemson 2, R. Burns 2, A. Szalay

More information

Reduction of parasitic currents in the DNS VOF code FS3D

Reduction of parasitic currents in the DNS VOF code FS3D M. Boger a J. Schlottke b C.-D. Munz a B. Weigand b Reduction of parasitic currents in the DNS VOF code FS3D Stuttgart, March 2010 a Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring

More information

Detailed Numerical Simulation of Liquid Jet in Cross Flow Atomization: Impact of Nozzle Geometry and Boundary Condition

Detailed Numerical Simulation of Liquid Jet in Cross Flow Atomization: Impact of Nozzle Geometry and Boundary Condition ILASS-Americas 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 23 Detailed Numerical Simulation of Liquid Jet in Cross Flow Atomization: Impact of Nozzle Geometry and

More information

SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES

SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES Yosuke Hasegawa Institute of Industrial Science The University of Tokyo Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan ysk@iis.u-tokyo.ac.jp

More information

An evaluation of a conservative fourth order DNS code in turbulent channel flow

An evaluation of a conservative fourth order DNS code in turbulent channel flow Center for Turbulence Research Annual Research Briefs 2 2 An evaluation of a conservative fourth order DNS code in turbulent channel flow By Jessica Gullbrand. Motivation and objectives Direct numerical

More information

WALL PRESSURE FLUCTUATIONS IN A TURBULENT BOUNDARY LAYER AFTER BLOWING OR SUCTION

WALL PRESSURE FLUCTUATIONS IN A TURBULENT BOUNDARY LAYER AFTER BLOWING OR SUCTION WALL PRESSURE FLUCTUATIONS IN A TURBULENT BOUNDARY LAYER AFTER BLOWING OR SUCTION Joongnyon Kim, Kyoungyoun Kim, Hyung Jin Sung Department of Mechanical Engineering, Korea Advanced Institute of Science

More information

Drop Impact on a Wet Surface: Computational Investigation of Gravity and Drop Shape

Drop Impact on a Wet Surface: Computational Investigation of Gravity and Drop Shape Drop Impact on a Wet Surface: Computational Investigation of Gravity and Drop Shape MURAT DINC and DONALD D. GRAY Department of Civil and Environmental Engineering West Virginia University P.O. Box 6103,

More information

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative

More information

A semi-implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows

A semi-implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows A semi-implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows M. Raessi, M. Bussmann*, and J. Mostaghimi Department of Mechanical and Industrial Engineering,

More information

LARGE EDDY SIMULATION OF MASS TRANSFER ACROSS AN AIR-WATER INTERFACE AT HIGH SCHMIDT NUMBERS

LARGE EDDY SIMULATION OF MASS TRANSFER ACROSS AN AIR-WATER INTERFACE AT HIGH SCHMIDT NUMBERS The 6th ASME-JSME Thermal Engineering Joint Conference March 6-, 3 TED-AJ3-3 LARGE EDDY SIMULATION OF MASS TRANSFER ACROSS AN AIR-WATER INTERFACE AT HIGH SCHMIDT NUMBERS Akihiko Mitsuishi, Yosuke Hasegawa,

More information

7. Basics of Turbulent Flow Figure 1.

7. Basics of Turbulent Flow Figure 1. 1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds

More information

The effects of confinement and inertia on the production of droplets

The effects of confinement and inertia on the production of droplets Rheologica Acta manuscript No. (will be inserted by the editor) Y. Renardy The effects of confinement and inertia on the production of droplets Received: date / Accepted: date Abstract Recent experiments

More information

Turbulent drag reduction by streamwise traveling waves

Turbulent drag reduction by streamwise traveling waves 51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA Turbulent drag reduction by streamwise traveling waves Armin Zare, Binh K. Lieu, and Mihailo R. Jovanović Abstract For

More information

Computational Fluid Dynamics 2

Computational Fluid Dynamics 2 Seite 1 Introduction Computational Fluid Dynamics 11.07.2016 Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016 Seite 2

More information

Oblique Drop Impact on Deep and Shallow Liquid

Oblique Drop Impact on Deep and Shallow Liquid 1 2 3 4 5 6 7 8 9 11 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Commun. Comput. Phys. doi: 10.4208/cicp.XXX.XXX Oblique Drop Impact on Deep and Shallow Liquid B. Ray 1, G. Biswas 1,2, and A. Sharma 3

More information

The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water Interface

The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water Interface Turbulence, Heat and Mass Transfer 4 K. Hanjalic, Y. Nagano and M. Tummers (Editors) 3 Begell House, Inc. The Role of Splatting Effect in High Schmidt Number Turbulent Mass Transfer Across an Air-Water

More information

Application of the immersed boundary method to simulate flows inside and outside the nozzles

Application of the immersed boundary method to simulate flows inside and outside the nozzles Application of the immersed boundary method to simulate flows inside and outside the nozzles E. Noël, A. Berlemont, J. Cousin 1, T. Ménard UMR 6614 - CORIA, Université et INSA de Rouen, France emeline.noel@coria.fr,

More information

DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT

DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT 10 th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT Bing-Chen Wang Department

More information

Simulating Interfacial Tension of a Falling. Drop in a Moving Mesh Framework

Simulating Interfacial Tension of a Falling. Drop in a Moving Mesh Framework Simulating Interfacial Tension of a Falling Drop in a Moving Mesh Framework Anja R. Paschedag a,, Blair Perot b a TU Berlin, Institute of Chemical Engineering, 10623 Berlin, Germany b University of Massachusetts,

More information

A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries

A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries Center for Turbulence Research Annual Research Briefs 2006 41 A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries By D. You AND P. Moin 1. Motivation

More information

NUMERICAL INVESTIGATION OF THERMOCAPILLARY INDUCED MOTION OF A LIQUID SLUG IN A CAPILLARY TUBE

NUMERICAL INVESTIGATION OF THERMOCAPILLARY INDUCED MOTION OF A LIQUID SLUG IN A CAPILLARY TUBE Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea ACTS-P00786 NUMERICAL INVESTIGATION OF THERMOCAPILLARY INDUCED MOTION OF A LIQUID SLUG IN A

More information

Generation of initial fields for channel flow investigation

Generation of initial fields for channel flow investigation Generation of initial fields for channel flow investigation Markus Uhlmann Potsdam Institut für Klimafolgenforschung, D-442 Potsdam uhlmann@pik-potsdam.de (Mai 2) In the framework of the DFG-funded research

More information

Simulation of T-junction using LBM and VOF ENERGY 224 Final Project Yifan Wang,

Simulation of T-junction using LBM and VOF ENERGY 224 Final Project Yifan Wang, Simulation of T-junction using LBM and VOF ENERGY 224 Final Project Yifan Wang, yfwang09@stanford.edu 1. Problem setting In this project, we present a benchmark simulation for segmented flows, which contain

More information

Turbulence - Theory and Modelling GROUP-STUDIES:

Turbulence - Theory and Modelling GROUP-STUDIES: Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence

More information

LIQUID FILM THICKNESS OF OSCILLATING FLOW IN A MICRO TUBE

LIQUID FILM THICKNESS OF OSCILLATING FLOW IN A MICRO TUBE Proceedings of the ASME/JSME 2011 8th Thermal Engineering Joint Conference AJTEC2011 March 13-17, 2011, Honolulu, Hawaii, USA AJTEC2011-44190 LIQUID FILM THICKNESS OF OSCILLATING FLOW IN A MICRO TUBE Youngbae

More information

A combined application of the integral wall model and the rough wall rescaling-recycling method

A combined application of the integral wall model and the rough wall rescaling-recycling method AIAA 25-299 A combined application of the integral wall model and the rough wall rescaling-recycling method X.I.A. Yang J. Sadique R. Mittal C. Meneveau Johns Hopkins University, Baltimore, MD, 228, USA

More information

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Published in Phys. Fluids 14, L73-L76 (22). Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Koji Fukagata, Kaoru Iwamoto, and Nobuhide Kasagi Department of Mechanical

More information

Nonlinear shape evolution of immiscible two-phase interface

Nonlinear shape evolution of immiscible two-phase interface Nonlinear shape evolution of immiscible two-phase interface Francesco Capuano 1,2,*, Gennaro Coppola 1, Luigi de Luca 1 1 Dipartimento di Ingegneria Industriale (DII), Università di Napoli Federico II,

More information

2.3 The Turbulent Flat Plate Boundary Layer

2.3 The Turbulent Flat Plate Boundary Layer Canonical Turbulent Flows 19 2.3 The Turbulent Flat Plate Boundary Layer The turbulent flat plate boundary layer (BL) is a particular case of the general class of flows known as boundary layer flows. The

More information

Numerical Studies of Droplet Deformation and Break-up

Numerical Studies of Droplet Deformation and Break-up ILASS Americas 14th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2001 Numerical Studies of Droplet Deformation and Break-up B. T. Helenbrook Department of Mechanical and

More information

Experiments on the perturbation of a channel flow by a triangular ripple

Experiments on the perturbation of a channel flow by a triangular ripple Experiments on the perturbation of a channel flow by a triangular ripple F. Cúñez *, E. Franklin Faculty of Mechanical Engineering, University of Campinas, Brazil * Correspondent author: fernandodcb@fem.unicamp.br

More information

ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS

ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS Karsten Lindegård Jensen 1, B. Mutlu Sumer 1, Giovanna Vittori 2 and Paolo Blondeaux 2 The pressure field in an oscillatory boundary layer

More information

Wall turbulence with arbitrary mean velocity profiles

Wall turbulence with arbitrary mean velocity profiles Center for Turbulence Research Annual Research Briefs 7 Wall turbulence with arbitrary mean velocity profiles By J. Jiménez. Motivation The original motivation for this work was an attempt to shorten the

More information

2. FLUID-FLOW EQUATIONS SPRING 2019

2. FLUID-FLOW EQUATIONS SPRING 2019 2. FLUID-FLOW EQUATIONS SPRING 2019 2.1 Introduction 2.2 Conservative differential equations 2.3 Non-conservative differential equations 2.4 Non-dimensionalisation Summary Examples 2.1 Introduction Fluid

More information

NEAR-WALL TURBULENCE-BUBBLES INTERACTIONS IN A CHANNEL FLOW AT Re =400: A DNS/LES INVESTIGATION

NEAR-WALL TURBULENCE-BUBBLES INTERACTIONS IN A CHANNEL FLOW AT Re =400: A DNS/LES INVESTIGATION ABSTRACT NEAR-WALL TURBULENCE-BUBBLES INTERACTIONS IN A CHANNEL FLOW AT Re =400: A DNS/LES INVESTIGATION D. Métrailler, S. Reboux and D. Lakehal ASCOMP GmbH Zurich, Technoparkstr. 1, Switzerland Metrailler@ascomp.ch;

More information

ROLE OF LARGE SCALE MOTIONS IN TURBULENT POISEUILLE AND COUETTE FLOWS

ROLE OF LARGE SCALE MOTIONS IN TURBULENT POISEUILLE AND COUETTE FLOWS 10 th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 ROLE OF LARGE SCALE MOTIONS IN TURBULENT POISEUILLE AND COUETTE FLOWS Myoungkyu Lee Robert D. Moser

More information

Direct numerical simulation of turbulence in a sheared air water flow with a deformable interface

Direct numerical simulation of turbulence in a sheared air water flow with a deformable interface Accepted for publication in J. Fluid Mech. 1 Direct numerical simulation of turbulence in a sheared air water flow with a deformable interface By M. Fulgosi 1, D. Lakehal 1, S. Banerjee 2 and V. De Angelis

More information

DNS, LES, and wall-modeled LES of separating flow over periodic hills

DNS, LES, and wall-modeled LES of separating flow over periodic hills Center for Turbulence Research Proceedings of the Summer Program 4 47 DNS, LES, and wall-modeled LES of separating flow over periodic hills By P. Balakumar, G. I. Park AND B. Pierce Separating flow in

More information

Turbulent boundary layer

Turbulent boundary layer Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic

More information

Turbulence Modeling I!

Turbulence Modeling I! Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!

More information

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,

More information

Numerical Simulation of Film Flow over an Inclined Plate: Effects of Solvent Properties and Contact Angle

Numerical Simulation of Film Flow over an Inclined Plate: Effects of Solvent Properties and Contact Angle Numerical Simulation of Film Flow over an Inclined Plate: Effects of Solvent Properties and Contact Angle Janine Carney and Rajesh Singh Multiphase Flow Science Workshop August 5-6, 214 Lakeview Golf Resort

More information

Development and analysis of a Lagrange-Remap sharp interface solver for stable and accurate atomization computations

Development and analysis of a Lagrange-Remap sharp interface solver for stable and accurate atomization computations ICLASS 2012, 12 th Triennial International Conference on Liquid Atomization and Spray Systems, Heidelberg, Germany, September 2-6, 2012 Development and analysis of a Lagrange-Remap sharp interface solver

More information

The JHU Turbulence Databases (JHTDB)

The JHU Turbulence Databases (JHTDB) The JHU Turbulence Databases (JHTDB) TURBULENT CHANNEL FLOW DATA SET Data provenance: J. Graham 1, M. Lee 2, N. Malaya 2, R.D. Moser 2, G. Eyink 1 & C. Meneveau 1 Database ingest and Web Services: K. Kanov

More information

arxiv: v1 [physics.flu-dyn] 16 Nov 2018

arxiv: v1 [physics.flu-dyn] 16 Nov 2018 Turbulence collapses at a threshold particle loading in a dilute particle-gas suspension. V. Kumaran, 1 P. Muramalla, 2 A. Tyagi, 1 and P. S. Goswami 2 arxiv:1811.06694v1 [physics.flu-dyn] 16 Nov 2018

More information

A Coupled VOF-Eulerian Multiphase CFD Model To Simulate Breaking Wave Impacts On Offshore Structures

A Coupled VOF-Eulerian Multiphase CFD Model To Simulate Breaking Wave Impacts On Offshore Structures A Coupled VOF-Eulerian Multiphase CFD Model To Simulate Breaking Wave Impacts On Offshore Structures Pietro Danilo Tomaselli Ph.d. student Section for Fluid Mechanics, Coastal and Maritime Engineering

More information

Numerical Simulation of the Hagemann Entrainment Experiments

Numerical Simulation of the Hagemann Entrainment Experiments CCC Annual Report UIUC, August 14, 2013 Numerical Simulation of the Hagemann Entrainment Experiments Kenneth Swartz (BSME Student) Lance C. Hibbeler (Ph.D. Student) Department of Mechanical Science & Engineering

More information

A comparison of viscoelastic stress wakes for 2D and 3D Newtonian drop deformation in a viscoelastic matrix under shear

A comparison of viscoelastic stress wakes for 2D and 3D Newtonian drop deformation in a viscoelastic matrix under shear A comparison of viscoelastic stress wakes for 2D and 3D Newtonian drop deformation in a viscoelastic matrix under shear S. Afkhami, P. Yue, and Y. Renardy Department of Mathematics, 460 McBryde Hall, Virginia

More information

The Turbulent Rotational Phase Separator

The Turbulent Rotational Phase Separator The Turbulent Rotational Phase Separator J.G.M. Kuerten and B.P.M. van Esch Dept. of Mechanical Engineering, Technische Universiteit Eindhoven, The Netherlands j.g.m.kuerten@tue.nl Summary. The Rotational

More information

A Discontinuous Galerkin Conservative Level Set Scheme for Simulating Turbulent Primary Atomization

A Discontinuous Galerkin Conservative Level Set Scheme for Simulating Turbulent Primary Atomization ILASS-Americas 3rd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA, May 011 A Discontinuous Galerkin Conservative Level Set Scheme for Simulating Turbulent Primary Atomization M.

More information

Exercise 5: Exact Solutions to the Navier-Stokes Equations I

Exercise 5: Exact Solutions to the Navier-Stokes Equations I Fluid Mechanics, SG4, HT009 September 5, 009 Exercise 5: Exact Solutions to the Navier-Stokes Equations I Example : Plane Couette Flow Consider the flow of a viscous Newtonian fluid between two parallel

More information

Figure 11.1: A fluid jet extruded where we define the dimensionless groups

Figure 11.1: A fluid jet extruded where we define the dimensionless groups 11. Fluid Jets 11.1 The shape of a falling fluid jet Consider a circular orifice of a radius a ejecting a flux Q of fluid density ρ and kinematic viscosity ν (see Fig. 11.1). The resulting jet accelerates

More information

Height function interface reconstruction algorithm for the simulation of boiling flows

Height function interface reconstruction algorithm for the simulation of boiling flows Computational Methods in Multiphase Flow VI 69 Height function interface reconstruction algorithm for the simulation of boiling flows M. Magnini & B. Pulvirenti Dipartimento di Ingegneria Energetica, Nucleare

More information

Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions

Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions June 30 - July 3, 2015 Melbourne, Australia 9 P-26 Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions Jungwoo Kim Department of Mechanical System Design Engineering

More information

, where the -function is equal to:

, where the -function is equal to: Paper ID ILASS08-000 ILASS08-9-4 ILASS 2008 Sep. 8-10, 2008, Como Lake, Italy BINARY COLLISION BETWEEN UNEQUAL SIZED DROPLETS. A NUMERICAL INVESTIGATION. N. Nikolopoulos 1, A. Theodorakakos 2 and G. Bergeles

More information

Direct numerical simulation of surface tension effects on interface dynamics in turbulence

Direct numerical simulation of surface tension effects on interface dynamics in turbulence ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 215 Direct numerical simulation of surface tension effects on interface dynamics in turbulence J.O. McCaslin

More information

FOUR-WAY COUPLED SIMULATIONS OF TURBULENT

FOUR-WAY COUPLED SIMULATIONS OF TURBULENT FOUR-WAY COUPLED SIMULATIONS OF TURBULENT FLOWS WITH NON-SPHERICAL PARTICLES Berend van Wachem Thermofluids Division, Department of Mechanical Engineering Imperial College London Exhibition Road, London,

More information

Flow Transition in Plane Couette Flow

Flow Transition in Plane Couette Flow Flow Transition in Plane Couette Flow Hua-Shu Dou 1,, Boo Cheong Khoo, and Khoon Seng Yeo 1 Temasek Laboratories, National University of Singapore, Singapore 11960 Fluid Mechanics Division, Department

More information

WALL RESOLUTION STUDY FOR DIRECT NUMERICAL SIMULATION OF TURBULENT CHANNEL FLOW USING A MULTIDOMAIN CHEBYSHEV GRID

WALL RESOLUTION STUDY FOR DIRECT NUMERICAL SIMULATION OF TURBULENT CHANNEL FLOW USING A MULTIDOMAIN CHEBYSHEV GRID WALL RESOLUTION STUDY FOR DIRECT NUMERICAL SIMULATION OF TURBULENT CHANNEL FLOW USING A MULTIDOMAIN CHEBYSHEV GRID Zia Ghiasi sghias@uic.edu Dongru Li dli@uic.edu Jonathan Komperda jonk@uic.edu Farzad

More information

DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING

DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING Yukinori Kametani Department of mechanical engineering Keio

More information

Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

More information

FLOW-NORDITA Spring School on Turbulent Boundary Layers1

FLOW-NORDITA Spring School on Turbulent Boundary Layers1 Jonathan F. Morrison, Ati Sharma Department of Aeronautics Imperial College, London & Beverley J. McKeon Graduate Aeronautical Laboratories, California Institute Technology FLOW-NORDITA Spring School on

More information

Investigation of an implicit solver for the simulation of bubble oscillations using Basilisk

Investigation of an implicit solver for the simulation of bubble oscillations using Basilisk Investigation of an implicit solver for the simulation of bubble oscillations using Basilisk D. Fuster, and S. Popinet Sorbonne Universités, UPMC Univ Paris 6, CNRS, UMR 79 Institut Jean Le Rond d Alembert,

More information

Turbulence Models for Flows with Free Surfaces and Interfaces

Turbulence Models for Flows with Free Surfaces and Interfaces AIAA JOURNAL Vol. 44, No. 7, July 2006 Turbulence Models for Flows with Free Surfaces and Interfaces Ebrahim Shirani, Ali Jafari, and Nasser Ashgriz University of Toronto, Toronto, Ontario M5S 3G8, Canada

More information

Simulation of a Pressure Driven Droplet Generator

Simulation of a Pressure Driven Droplet Generator Simulation of a Pressure Driven Droplet Generator V. Mamet* 1, P. Namy 2, N. Berri 1, L. Tatoulian 1, P. Ehouarn 1, V. Briday 1, P. Clémenceau 1 and B. Dupont 1 1 DBV Technologies, 2 SIMTEC *84 rue des

More information

Numerical analysis of fluid flow and heat transfer in 2D sinusoidal wavy channel

Numerical analysis of fluid flow and heat transfer in 2D sinusoidal wavy channel Numerical analysis of fluid flow and heat transfer in 2D sinusoidal wavy channel Arunanshu Chakravarty 1* 1 CTU in Prague, Faculty of Mechanical Engineering, Department of Process Engineering,Technická

More information

Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step

Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step Copyright c 2004 Tech Science Press CMC, vol.1, no.3, pp.275-288, 2004 Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step B. Wang 1, H.Q. Zhang 1, C.K. Chan 2 and X.L.

More information

Transition to turbulence in plane Poiseuille flow

Transition to turbulence in plane Poiseuille flow Proceedings of the 55th Israel Annual Conference on Aerospace Sciences, Tel-Aviv & Haifa, Israel, February 25-26, 2015 ThL2T5.1 Transition to turbulence in plane Poiseuille flow F. Roizner, M. Karp and

More information

Chapter 9: Differential Analysis

Chapter 9: Differential Analysis 9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control

More information

Patterns of Turbulence. Dwight Barkley and Laurette Tuckerman

Patterns of Turbulence. Dwight Barkley and Laurette Tuckerman Patterns of Turbulence Dwight Barkley and Laurette Tuckerman Plane Couette Flow Re = U gap/2 ν Experiments by Prigent and Dauchot Re400 Z (Spanwise) 40 24 o Gap 2 Length 770 X (Streamwise) Examples: Patterns

More information

* Ho h h (3) D where H o is the water depth of undisturbed flow, D is the thickness of the bridge deck, and h is the distance from the channel floor t

* Ho h h (3) D where H o is the water depth of undisturbed flow, D is the thickness of the bridge deck, and h is the distance from the channel floor t The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September -6, 01 Numerical simulation of hydrodynamic loading on submerged rectangular bridge decks

More information

Modelling of Break-up and Coalescence in Bubbly Two-Phase Flows

Modelling of Break-up and Coalescence in Bubbly Two-Phase Flows Modelling of Break-up and Coalescence in Bubbly Two-Phase Flows Simon Lo and Dongsheng Zhang CD-adapco, Trident Park, Didcot OX 7HJ, UK e-mail: simon.lo@uk.cd-adapco.com Abstract Numerical simulations

More information

Eddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr):

Eddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr): AdOc 4060/5060 Spring 2013 Chris Jenkins Eddy viscosity Turbulence (video 1hr): http://cosee.umaine.edu/programs/webinars/turbulence/?cfid=8452711&cftoken=36780601 Part B Surface wind stress Wind stress

More information

Table of Contents. Foreword... xiii. Preface... xv

Table of Contents. Foreword... xiii. Preface... xv Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

More information

Chapter 9: Differential Analysis of Fluid Flow

Chapter 9: Differential Analysis of Fluid Flow of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known

More information

- Marine Hydrodynamics. Lecture 4. Knowns Equations # Unknowns # (conservation of mass) (conservation of momentum)

- Marine Hydrodynamics. Lecture 4. Knowns Equations # Unknowns # (conservation of mass) (conservation of momentum) 2.20 - Marine Hydrodynamics, Spring 2005 Lecture 4 2.20 - Marine Hydrodynamics Lecture 4 Introduction Governing Equations so far: Knowns Equations # Unknowns # density ρ( x, t) Continuity 1 velocities

More information

Chapter 1 Transition to Three-dimensional Waves in Cocurrent Gas-liquid Flows

Chapter 1 Transition to Three-dimensional Waves in Cocurrent Gas-liquid Flows Chapter 1 Transition to Three-dimensional Waves in Cocurrent Gas-liquid Flows W. C. Kuru, M. Sangalli and M. J. McCready Abstract The transition from two-dimensional to three-dimensional waves on the interface

More information

Shear-induced rupturing of a viscous drop in a Bingham liquid

Shear-induced rupturing of a viscous drop in a Bingham liquid J. Non-Newtonian Fluid Mech. 95 (2000) 235 251 Shear-induced rupturing of a viscous drop in a Bingham liquid Jie Li, Yuriko Y. Renardy Department of Mathematics and ICAM, Virginia Polytechnic Institute

More information

Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell

Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows Lyon, July 2007 Paper reference : ISAIF8-00130 Analysis of Turbulent Free Convection

More information

Absorption of gas by a falling liquid film

Absorption of gas by a falling liquid film Absorption of gas by a falling liquid film Christoph Albert Dieter Bothe Mathematical Modeling and Analysis Center of Smart Interfaces/ IRTG 1529 Darmstadt University of Technology 4th Japanese-German

More information

Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles

Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction &

More information

NUMERICAL SIMULATION OF MICRO-FILTRATION OF OIL-IN-WATER EMULSIONS. Tohid Darvishzadeh

NUMERICAL SIMULATION OF MICRO-FILTRATION OF OIL-IN-WATER EMULSIONS. Tohid Darvishzadeh NUMERICAL SIMULATION OF MICRO-FILTRATION OF OIL-IN-WATER EMULSIONS By Tohid Darvishzadeh A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree

More information

Interpreting Differential Equations of Transport Phenomena

Interpreting Differential Equations of Transport Phenomena Interpreting Differential Equations of Transport Phenomena There are a number of techniques generally useful in interpreting and simplifying the mathematical description of physical problems. Here we introduce

More information

GRAVITY-DRIVEN MOTION OF A SWARM OF BUBBLES IN A VERTICAL PIPE

GRAVITY-DRIVEN MOTION OF A SWARM OF BUBBLES IN A VERTICAL PIPE 27th International Conference on Parallel Computational Fluid Dynamics Parallel CFD2015 GRAVITY-DRIVEN MOTION OF A SWARM OF BUBBLES IN A VERTICAL PIPE Néstor Balcázar, Oriol Lehmkuhl, Jesús Castro, Joaquim

More information

Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace

Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Adapted from Publisher: John S. Wiley & Sons 2002 Center for Scientific Computation and

More information

Uncertainty quantification for RANS simulation of flow over a wavy wall

Uncertainty quantification for RANS simulation of flow over a wavy wall Uncertainty quantification for RANS simulation of flow over a wavy wall Catherine Gorlé 1,2,3, Riccardo Rossi 1,4, and Gianluca Iaccarino 1 1 Center for Turbulence Research, Stanford University, Stanford,

More information

Physical Properties of Fluids

Physical Properties of Fluids Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel

More information

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

More information

Validation analyses of advanced turbulence model approaches for stratified two-phase flows

Validation analyses of advanced turbulence model approaches for stratified two-phase flows Computational Methods in Multiphase Flow VIII 361 Validation analyses of advanced turbulence model approaches for stratified two-phase flows M. Benz & T. Schulenberg Institute for Nuclear and Energy Technologies,

More information

Model-based analysis of polymer drag reduction in a turbulent channel flow

Model-based analysis of polymer drag reduction in a turbulent channel flow 2013 American Control Conference ACC Washington, DC, USA, June 17-19, 2013 Model-based analysis of polymer drag reduction in a turbulent channel flow Binh K. Lieu and Mihailo R. Jovanović Abstract We develop

More information

Turbulentlike Quantitative Analysis on Energy Dissipation in Vibrated Granular Media

Turbulentlike Quantitative Analysis on Energy Dissipation in Vibrated Granular Media Copyright 011 Tech Science Press CMES, vol.71, no., pp.149-155, 011 Turbulentlike Quantitative Analysis on Energy Dissipation in Vibrated Granular Media Zhi Yuan Cui 1, Jiu Hui Wu 1 and Di Chen Li 1 Abstract:

More information

Computation of turbulent Prandtl number for mixed convection around a heated cylinder

Computation of turbulent Prandtl number for mixed convection around a heated cylinder Center for Turbulence Research Annual Research Briefs 2010 295 Computation of turbulent Prandtl number for mixed convection around a heated cylinder By S. Kang AND G. Iaccarino 1. Motivation and objectives

More information

Numerical Heat and Mass Transfer

Numerical Heat and Mass Transfer Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis

More information

INTERFACIAL WAVE BEHAVIOR IN OIL-WATER CHANNEL FLOWS: PROSPECTS FOR A GENERAL UNDERSTANDING

INTERFACIAL WAVE BEHAVIOR IN OIL-WATER CHANNEL FLOWS: PROSPECTS FOR A GENERAL UNDERSTANDING 1 INTERFACIAL WAVE BEHAVIOR IN OIL-WATER CHANNEL FLOWS: PROSPECTS FOR A GENERAL UNDERSTANDING M. J. McCready, D. D. Uphold, K. A. Gifford Department of Chemical Engineering University of Notre Dame Notre

More information

Exercise: concepts from chapter 10

Exercise: concepts from chapter 10 Reading:, Ch 10 1) The flow of magma with a viscosity as great as 10 10 Pa s, let alone that of rock with a viscosity of 10 20 Pa s, is difficult to comprehend because our common eperience is with s like

More information

Periodic planes v i+1 Top wall u i. Inlet. U m y. Jet hole. Figure 2. Schematic of computational domain.

Periodic planes v i+1 Top wall u i. Inlet. U m y. Jet hole. Figure 2. Schematic of computational domain. Flow Characterization of Inclined Jet in Cross Flow for Thin Film Cooling via Large Eddy Simulation Naqavi, I.Z. 1, Savory, E. 2 and Martinuzzi, R. J. 3 1,2 The Univ. of Western Ontario, Dept. of Mech.

More information

CFD analysis of the transient flow in a low-oil concentration hydrocyclone

CFD analysis of the transient flow in a low-oil concentration hydrocyclone CFD analysis of the transient flow in a low-oil concentration hydrocyclone Paladino, E. E. (1), Nunes, G. C. () and Schwenk, L. (1) (1) ESSS Engineering Simulation and Scientific Software CELTA - Rod SC-41,

More information

Fluid Mechanics Theory I

Fluid Mechanics Theory I Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to

More information

AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS

AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS Hierarchy of Mathematical Models 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 2 / 29

More information